The XD Program System and Calculation of Properties

1
The XD Program System andCalculation of
Properties
Jyväskylä Summer School on Charge Density August
2007
Louis J Farrugia
2
Jyväskylä Summer School on Charge Density August
2007
The XD Program System
The XD program system is a comprehensive computer
program package for multipole refinement,
topological analysis of charge densities and
evaluation of intermolecular energies from
experimental or theoretical structure factors.
XD uses THREE primary input files
XD.INP/XD.RES - contains the refined
parameters XD.HKL - the reflection data as F or
F2 with sigma's and optional dir cosines XD.MAS
- contains all the program instructions
A. Volkov, P. Macchi, L. J. Farrugia, C. Gatti,
P. R. Mallinson, T. Richter, T. Koritsanszky
(2006).
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Jyväskylä Summer School on Charge Density August
2007
The XD Program System
module task
XDINI importing data to XD
XDLSM least-squares refinement
XDGEOM calculation of tables of geometries, ADPs, multipolar parameters and errors
XFOUR calculation of Fourier maps
XDFFT fast Fourier transform program
XDPROP calculation of one-electron properties
XDGRAPH visualization
TOPXD full topological analysis of crystal structures
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Jyväskylä Summer School on Charge Density August
2007
The XD Program System
5
Jyväskylä Summer School on Charge Density August
2007
The XD Program System
6
Jyväskylä Summer School on Charge Density August
2007
The XDINI Program
The XDINI program provides a link between
"standard" refinement programs like SHELXL or the
standard crystallographic file format (CIF) and
the XD program system. XDINI reads either
SHELX.INS SHELX.HKL (or XD.CIF XD.FCF)
and writes default versions of XD.INP, XD.MAS,
XD.HKL. It needs to know (a) format you are
using (b) ID name (XD) (c) the database you wish
to use.
Command line XDINI ltnamegt ltformatgt ltdatabank
codegt XDINI xd shelx SCM
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Jyväskylä Summer School on Charge Density August
2007
Choice of the Databank
xd.bnk_RHF_CR (BANK CR)
CHFW Non relativistic wave functions (H-Kr,
including ions) Clementi, E. Roetti, C. (1974).
At. Data Nucl. Data Tables, 14, 177-478 RDSD E.
Clementi and D. L. Raimondi, J. Chem. Phys. 38,
2686-2689 (1963). Analytical Fit International
Tables for Crystallography
xd.bnk_RHF_BBB (BANK BBB)
CHFW Non relativistic wave functions (H-Xe) C.
F. Bunge, J. A. Barrientos, A. V. Bunge At. Data
Nucl. Data Tables, 53, 113-162 (1993). RDSD E.
Clementi and D. L. Raimondi, J. Chem. Phys. 38,
2686-2689 (1963). Analytical Fit International
Tables for Crystallography
xd.bnk_RDF_SCM (BANK SCM)
CHFW Relativistic wave functions (H-Xe,
including ions) Z. Su and P. Coppens Acta Cryst.,
A54, 646 (1998) P. Macchi and P. Coppens Acta
Cryst., A57, 656 (2001). RDSD E. Clementi and D.
L. Raimondi, J. Chem. Phys. 38, 2686-2689
(1963). Analytical Fit Su, Z. Coppens, P. Acta
Cryst 1997, A53, 749, Macchi, P. Coppens, P.
Acta Cryst., 2001, A57, 656
xd.bnk_PBE-QZ4P-ZORA (BANK VM)
CHFW Relativistic wave functions (H-Cf)
unpublished RDSD E. Clementi and D. L. Raimondi,
J. Chem. Phys. 38, 2686-2689 (1963). Analytical
Fit Macchi, P. Volkov, A. unpublished
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
ltnamegt
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
number of atoms
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
Parameters for atom O(1)
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
12
Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
positional parameters
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
Occupancy - not refinable !
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
anisotropic thermal parameters U11 U22 U33 U12
U13 U23
15
Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
multipole parameters - currently only Pv and P00
are present
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Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
Kappa parameters
17
Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
Extinction parameters
18
Jyväskylä Summer School on Charge Density August
2007
The XD.INP Parameter File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D PARAMETER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! XDPARFILE
VERSION 2 XD MODEL 0 0 0 0 LIMITS
nat 2000 ntx 31 lmx 4 nzz 30 nto 0 nsc 20
ntb 20 nov 2500 USAGE 20 0 0 4 0
1 0 0 4 0 0 0 0 0 0.000000
0.000000 0.000000 0.000000 0.000000 0.000000
0.000000 0.000E00 0.000000 0.000000 0.000000
0.000000 0.000000 0.000000 O(1) 3 2 13
1 6 2 1 1 0 0 0 0.202009 0.200013
0.479127 1.0000 0.025050 0.012910 0.009490
-0.010960 0.000890 -0.000330 6.0000
0.0000 O(2) 3 2 6 2 13 2 1 1 0 0
0 -0.004865 0.031916 0.359431 1.0000 0.023710
0.015640 0.007150 -0.007000 -0.000440
-0.001250 6.0000 0.0000 . . . H(7) 3 2
5 20 19 1 4 4 0 0 0 0.930190 0.964298
0.213487 1.0000 0.024890 0.000000 0.000000
0.000000 0.000000 0.000000 1.0000 0.0000 1
1.000000 1.000000 1.000000 1.000000 1.000000
1.000000 2 1.000000 1.000000 1.000000
1.000000 1.000000 1.000000 3 1.000000
1.000000 1.000000 1.000000 1.000000 1.000000
4 1.200000 1.200000 1.200000 1.200000
1.200000 1.200000 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.0000E00 0.0000E00
0.0000E00 0.0000E00 0.117148E01
Overall scale factor
19
Jyväskylä Summer School on Charge Density August
2007
The XD.HKL Reflection File
XD F2 NDAT 6 -5 -7 1
1 5.300 0.790 -5 -7 2 1
74.050 2.480 -5 -7 3 1 2.740
1.540 -5 -7 4 1 11.410
10.700 -5 -6 1 1 21.890 1.880
-5 -6 2 1 0.540 1.210 -5 -6
3 1 5.140 0.860 -5 -6 4 1
3.090 1.030 -5 -6 5 1
94.190 2.830 -5 -6 6 1 17.450
13.830 -5 -5 1 1 2.680
1.130 . . .
Data may be presented either as F or F2 (NOTE in
current version the sigma cutoff is applied
BEFORE conversion) Several batch scale factors
can be refined Phases may optionally be present
(phase angle in radians, NDAT -7)
20
Jyväskylä Summer School on Charge Density August
2007
The XD.MAS Control File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D MASTER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! TITLE
XD CELL 3.6782 7.5991 12.4999 85.662
88.029 84.225 WAVE 0.71073 CELLSD
0.0003 0.0005 0.0008 0.003 0.003
0.002 LATT C P SYMM 1/2X,1/2-Y,1/2z BANK
SCM !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! MODULE
XDLSM SELECT model 0 2 1 0 based_on F test
verbose 1 SELECT cycle -1 dampk 1. cmin 0.6 cmax
1. eigcut 1.d-09 convcrit 0.0 SAVE deriv lsqmat
cormat SOLVE inv diag cond !------------------
--------------------------------------------------
---------- SCAT CORE SPHV DEFV 1S 2S 3S 4S
2P 3P 4P 3D 4D 4F 5S 5P 6S 6P 5D 7S
6D 5F DELF' DELF'' NSCTL O CHFW CHFW CSZD
2 -2 0 0 -4 0 0 0 0 0 0 0
0 0 0 0 0 0 0.0110 0.0060 0.580 N
CHFW CHFW CSZD 2 -2 0 0 -3 0 0 0
0 0 0 0 0 0 0 0 0 0 0.0060
0.0030 0.936 C CHFW CHFW CSZD 2 -2 0
0 -2 0 0 0 0 0 0 0 0 0 0 0
0 0 0.0030 0.0020 0.665 H CHFW CHFW
CSZD -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0.0000 0.0000
-0.374 END SCAT . . END XDLSM
Divided into sections - one main section and
eight other sections giving commands for the
main program modules.
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Jyväskylä Summer School on Charge Density August
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The XD.MAS Control File
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ! ltltlt X D MASTER
FILE gtgtgt Revision 5.39 (Jun 5 2007)
24-Jun-06! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! TITLE
XD CELL 3.6782 7.5991 12.4999 85.662
88.029 84.225 WAVE 0.71073 CELLSD
0.0003 0.0005 0.0008 0.003 0.003
0.002 LATT C P SYMM 1/2X,1/2-Y,1/2z BANK
SCM !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! MODULE
XDLSM SELECT model 0 2 1 0 based_on F test
verbose 1 SELECT cycle -1 dampk 1. cmin 0.6 cmax
1. eigcut 1.d-09 convcrit 0.0 SAVE deriv lsqmat
cormat SOLVE inv diag cond !------------------
--------------------------------------------------
---------- SCAT CORE SPHV DEFV 1S 2S 3S 4S
2P 3P 4P 3D 4D 4F 5S 5P 6S 6P 5D 7S
6D 5F DELF' DELF'' NSCTL O CHFW CHFW CSZD
2 -2 0 0 -4 0 0 0 0 0 0 0
0 0 0 0 0 0 0.0110 0.0060 0.580 N
CHFW CHFW CSZD 2 -2 0 0 -3 0 0 0
0 0 0 0 0 0 0 0 0 0 0.0060
0.0030 0.936 C CHFW CHFW CSZD 2 -2 0
0 -2 0 0 0 0 0 0 0 0 0 0 0
0 0 0.0030 0.0020 0.665 H CHFW CHFW
CSZD -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0.0000 0.0000
-0.374 END SCAT . . END XDLSM
Everything between MODULE XDLSM and END XDLSM
refers to commands and/or information for the
refinement program XDLSM. The XDLSM indicates
that this module is activated - a common usage in
XD
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Jyväskylä Summer School on Charge Density August
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The XDLSM Commands
MODULE XDLSM SELECT model 0 2 1 0 based_on
F test verbose 1 SELECT cycle -1 dampk 1. cmin
0.6 cmax 1. eigcut 1.d-09 convcrit 0.0 SAVE
deriv lsqmat cormat SOLVE inv diag
cond !-------------------------------------------
----------------------------------- SCAT CORE
SPHV DEFV 1S 2S 3S 4S 2P 3P 4P 3D 4D
4F 5S 5P 6S 6P 5D 7S 6D 5F DELF'
DELF'' NSCTL O CHFW CHFW CSZD 2 -2 0
0 -4 0 0 0 0 0 0 0 0 0 0 0
0 0 0.0110 0.0060 0.580 N CHFW CHFW
CSZD 2 -2 0 0 -3 0 0 0 0 0 0
0 0 0 0 0 0 0 0.0060 0.0030
0.936 C CHFW CHFW CSZD 2 -2 0 0 -2
0 0 0 0 0 0 0 0 0 0 0 0 0
0.0030 0.0020 0.665 H CHFW CHFW CSZD -1
0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0.0000 0.0000 -0.374 END
SCAT . . END XDLSM
XDLSM is a standard full-matrix least-squares
refinement program, which can refine on F or F2
(based_on F/F2). Few sophisticated
features. Convergence criterion - refinement
stops when I/sig(I) lt convcrit The SCAT table
defines the scattering model used for each atomic
type. The numbers define the occupations of the
HF orbitals - negative numbers mean that those
electrons are defined as the valence electrons,
otherwise they are assumed to be core. More than
one entry for a particular element is
allowed. In general, the SCAT table written by
the import program XDINI will be satisfactory for
an initial model.
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Jyväskylä Summer School on Charge Density August
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The ATOM Table
ATOM ATOM0 AX1 ATOM1 ATOM2 AX2
R/L TP TBL KAP LMX SITESYM CHEMCON O(1) C(1)
X O(1) N(1) Y R 2 1 1 4
m N(1) C(1) Z N(1) O(1) Y
R 2 2 2 4 mm2 C(1) N(1)
X C(1) O(1) Y R 2 3 3 4
m H(1) N(1) Z H(1)
C(1) Y R 1 4 4 1 cyl
H(2) N(1) Z H(2) C(1) Y R
1 4 4 1 cyl H(3) C(1)
Z H(3) O(1) Y R 1 4 4 1
cyl DUM0 0.0000 0.0000 0.0000 END ATOM
The ATOM table defines the local coordinate
system used for each atom, as well as identifying
the scattering type and Kappa set for that atom.
Limits on the multipole expansion, thermal motion
description and chemical constraints are also
applied here. In general, the ATOM table written
by the import program XDINI will be NOT
satisfactory for an initial model.
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Jyväskylä Summer School on Charge Density August
2007
The ATOM Table
ATOM ATOM0 AX1 ATOM1 ATOM2 AX2
R/L TP TBL KAP LMX SITESYM CHEMCON O(1) C(1)
X O(1) N(1) Y R 2 1 1 4
m N(1) C(1) Z N(1) O(1) Y
R 2 2 2 4 mm2 C(1) N(1)
X C(1) O(1) Y R 2 3 3 4
m H(1) N(1) Z H(1)
C(1) Y R 1 4 4 1 cyl
H(2) N(1) Z H(2) C(1) Y R
1 4 4 1 cyl H(3) C(1)
Z H(3) O(1) Y R 1 4 4 1
cyl DUM0 0.0000 0.0000 0.0000 END ATOM
C atom m
O atom m
N atom mm2
H atom cyl
Formamide HC(O)NH2
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Jyväskylä Summer School on Charge Density August
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The KEY Table
KEY xyz --U2-- ----U3---- ------U4------- M-
-D- --Q-- ---O--- ----H---- O(1) 000 000000
0000000000 000000000000000 00 000 00000 0000000
000000000 N(1) 000 000000 0000000000
000000000000000 00 000 00000 0000000
000000000 C(1) 000 000000 0000000000
000000000000000 00 000 00000 0000000
000000000 H(1) 000 000000 0000000000
000000000000000 00 000 00000 0000000
000000000 H(2) 000 000000 0000000000
000000000000000 00 000 00000 0000000
000000000 H(3) 000 000000 0000000000
000000000000000 00 000 00000 0000000
000000000 KAPPA 000000 KAPPA 000000 KAPPA
000000 KAPPA 000000 EXTCN 0000000 OVTHP
0 SCALE 1 END KEY
The KEY table defines which parameters are to be
refined. "0" means don't refine and any other
entry, usually "1" means refine. The layout for
the atoms is self explanatory. The XD manual
tutorial gives the order in which the U's and
multipole parameters are given. In general, the
KEY table written by the import program XDINI
will be satisfactory for an initial model, but is
the part of the input which needs changing most.
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Jyväskylä Summer School on Charge Density August
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The XDLSM Commands
!GROUP2 atom1 atom2 ... KEEP kappa 1 2 3
4 KEEP charge group1 !KEEP rigid
group1 !RESET bond C(1) H(1) 1.09 ... WEIGHT
-2.0 .0 .0 .0 .0 0.3333 !SWAT g 0.00 U 0.00 SKIP
obs 0. 1.d10 sigobs 3. 1.d06 sinthl 0.
2. !PRINT sinthl .0 2. obs 0. 15. delta 0. 10.
del 80 100 extcn 80. 100. abssc !EXTCN iso
aniso type_1 type_2 type_3 distr_g distr_l
msc_0 msc_1 DMSDA 1.1 1.8 FOUR fmod1 4 2
0 0 fmod2 -1 2 0 0 !CON num1 par1/iat1 num2
par2/iat2 ... num0
In XDLSM (as in all programs) placing an "!"
mark as the first character comments out the
commands. The KEEP kappa command ensures that
the kappa' parameters for all l values of the
deformation valence are the same The KEEP charge
ensures that the sum of the monopole populations
Pv equals the total valence population.
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Jyväskylä Summer School on Charge Density August
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The Results of Refinement
A set of positional, thermal motion and
multipole parameters which provide the best fit
to the data. These parameters can be used to
reconstruct and analyse the electron density (do
not use Fourier methods). CAVEATS 1. Because of
the complexity of the model, least-squares
procedure may not provide a unique solution. 2.
The refinement of the mutipole parameters may be
difficult if the structure is non-centrosymmetric,
because of correlations between phases and
odd-order multipoles. 3. The accuracy of the
final parameters depends crucially on the quality
of the experimental data. Systematic errors are
the worst, but even random errors can degrade the
results
A. El Hauouzi et al (1996) Acta Cryst. A52,
291. C. Lecomte et al (1999) Acta Cryst.A55 1038.
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Jyväskylä Summer School on Charge Density August
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An Interesting Tale ...
In 1992, Howard et al reported a charge density
study on 2-methyl-4-nitroaniline (MNA) which
showed a threefold enhancement of the molecular
dipole moment on crystallisation, to 23D with an
error of 8D. Became a classic reference.
New results of Whitten, Spackman et al in 2006
suggest that this result is quite unreasonable.
After a very careful data collection and
refinement, they estimate that the true result is
12(1) D, i.e. an enhancement of 25-30. This
result is also close to their theoretical work.
The discrepancies with the previous work is a
result of unstable refinement of the scale factor
and use of anisotropic thermal parameters for the
H atoms.
S. T. Howard et al (1992) J. Chem. Phys. 97,
5616. A. E. Whitten, M. A Spackman et al (2006)
J. Phys. Chem. A, 110, 8763.
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Jyväskylä Summer School on Charge Density August
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Fourier Maps in XD
Two programs in XD XDFFT calculates Fourier
over whole unit cell used for reporting
residuals XDFOUR can calculate Fourier in an
arbitary plane useful for investigations
FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0 MODULE
XDFFT SELECT fobs fmod1 fmod2 snlmin 0.
snlmax 2. sig 3. phase 0. SELECT gridsize 0.2
scale 1. npeak 10 nhole 10 neutron gridf
peakf END XDFFT MODULE XDFOUR SELECT fobs
fmod1 fmod2 print snlmin 0. snlmax 2. GRID
3-points perp cryst ATOM label ato(1) symm 1
trans 0 0 0 mark on plot ATOM label ato(2)
symm 1 trans 0 0 0 mark on plot ATOM label
ato(3) symm 1 trans 0 0 0 mark on plot LIMITS
xmin -2.0 xmax 2.0 nx 50 LIMITS ymin -2.0 ymax
2.0 ny 50 LIMITS zmin 0.0 zmax 0.0 nz 1
END XDFOUR
command in XDLSM to write XD.FOU file
XD.FOU contains Fobs and two types of Fcalc based
on the models indicated in the FOUR command
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Jyväskylä Summer School on Charge Density August
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Fourier Maps in XD
Two programs in XD XDFFT calculates Fourier
over whole unit cell used for reporting
residuals XDFOUR can calculate Fourier in an
arbitary plane useful for investigations
FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0 MODULE
XDFFT SELECT fobs fmod1 fmod2 snlmin 0.
snlmax 2. sig 3. phase 0. SELECT gridsize 0.2
scale 1. npeak 10 nhole 10 neutron gridf
peakf END XDFFT MODULE XDFOUR SELECT fobs
fmod1 fmod2 print snlmin 0. snlmax 2. GRID
3-points perp cryst ATOM label ato(1) symm 1
trans 0 0 0 mark on plot ATOM label ato(2)
symm 1 trans 0 0 0 mark on plot ATOM label
ato(3) symm 1 trans 0 0 0 mark on plot LIMITS
xmin -2.0 xmax 2.0 nx 50 LIMITS ymin -2.0 ymax
2.0 ny 50 LIMITS zmin 0.0 zmax 0.0 nz 1
END XDFOUR
command in XDLSM to write XD.FOU file
fmod1 4 2 0 0 means (a) multipole model up to
l 4 (b) thermal motion up to anisotropic (c)
no anomalous dispersion (d) no extinction
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Jyväskylä Summer School on Charge Density August
2007
Fourier Maps in XD
Two programs in XD XDFFT calculates Fourier
over whole unit cell used for reporting
residuals XDFOUR can calculate Fourier in an
arbitary plane useful for investigations
FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0 MODULE
XDFFT SELECT fobs fmod1 fmod2 snlmin 0.
snlmax 2. sig 3. phase 0. SELECT gridsize 0.2
scale 1. npeak 10 nhole 10 neutron gridf
peakf END XDFFT MODULE XDFOUR SELECT fobs
fmod1 fmod2 print snlmin 0. snlmax 2. GRID
3-points perp cryst ATOM label ato(1) symm 1
trans 0 0 0 mark on plot ATOM label ato(2)
symm 1 trans 0 0 0 mark on plot ATOM label
ato(3) symm 1 trans 0 0 0 mark on plot LIMITS
xmin -2.0 xmax 2.0 nx 50 LIMITS ymin -2.0 ymax
2.0 ny 50 LIMITS zmin 0.0 zmax 0.0 nz 1
END XDFOUR
command in XDLSM to write XD.FOU file
fmod1 1 2 0 0 means (a) spherical atom model
(b) thermal motion up to anisotropic (c) no
anomalous dispersion (d) no extinction
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Jyväskylä Summer School on Charge Density August
2007
Fourier Maps in XD
Two programs in XD XDFFT calculates Fourier
over whole unit cell used for reporting
residuals XDFOUR can calculate Fourier in an
arbitary plane useful for investigations
FOUR fmod1 4 2 0 0 fmod2 -1 2 0 0 MODULE
XDFFT SELECT fobs fmod1 fmod2 snlmin 0.
snlmax 2. sig 3. phase 0. SELECT gridsize 0.2
scale 1. npeak 10 nhole 10 neutron gridf
peakf END XDFFT MODULE XDFOUR SELECT fobs
fmod1 fmod2 print snlmin 0. snlmax 2. GRID
3-points perp cryst ATOM label ato(1) symm 1
trans 0 0 0 mark on plot ATOM label ato(2)
symm 1 trans 0 0 0 mark on plot ATOM label
ato(3) symm 1 trans 0 0 0 mark on plot LIMITS
xmin -2.0 xmax 2.0 nx 50 LIMITS ymin -2.0 ymax
2.0 ny 50 LIMITS zmin 0.0 zmax 0.0 nz 1
END XDFOUR
fobs fmod1 means calculate a difference Fourier
with coefficients based on Fcalc from model 1 and
Fobs this map is a full difference Fourier and
should be featureless
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Jyväskylä Summer School on Charge Density August
2007
Fourier Maps in XD
fobs fmod1 Residual map These are very
important for checking the quality of data and of
the refinement Contours at 0.05eÅ-3
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Jyväskylä Summer School on Charge Density August
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Fourier Maps in XD
fobs fmod2 Experimental deformation map These
are equivalent to the difference maps obtained
with a SHELX refinement. Shows the bonding
density peaks Contours at 0.05eÅ-3
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Jyväskylä Summer School on Charge Density August
2007
Fourier Maps in XD
fmod1 fmod2 Dynamic model map These show the
difference between Fcalc (spherical) and Fcalc
(multipole). Similar to experimental
deformation map. Does not contain experimental
noise, but does contain effects of thermal
motion. Contours at 0.05eÅ-3
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Jyväskylä Summer School on Charge Density August
2007
XDPROP calculation of properties
XDPROP performs a number of tasks. The input
parameters are the multipole populations from the
refinement program XDLSM. From these the
static density (and associated properties) can be
computed. topological analysis finds critical
points in scalar field (density or Laplacian) and
seaches for bond paths (molecular graph).
Graphical display of gradient vector plots. Gives
the topology of the molecule extracted from the
crystal Program TOPXD gives the topology of the
crystal. atomic charges and higher moments
these can be calculated in a number of ways,
either from the multipole parameters of by
numerical integration of the derived
density interaction energies between two or
more fragments of the total lattice energy d-orbi
tal populations from multipole
parameters Properties are obtained as lists of
numbers and also in graphical form (2D and 3D
maps).
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Jyväskylä Summer School on Charge Density August
2007
XDPROP topological analysis
Concepts of topological analysis dealt with in
another lecture. Shown here is the molecular
graph for formamide, giving the bond paths
(in gold), the bond critical points (in red) and
the eigenvectors of the Hessian (red major
axis, green minor axis of curvature). This
POV-Ray picture is producesd by the WinXD GUI
CPSEARCH BOND C(1) H(3) CPSEARCH SHELL O(1)
RMIN 1.20 RMAX 1.20 NRAD 1 NANG 15 15 CUT
0.01 CPSEARCH POINT 1.2 -0.3 1.3 CPSEARCH
START xd.cps cpsearch bond rmin 0.9 rmax
1.7 BPATH O(1) C(1) ALGRITHM 2 BPATH N(1)
C(1) ALGRITHM 2 BPATH N(1) H(1) ALGRITHM
2 BPATH N(1) H(2) ALGRITHM 2 BPATH C(1) H(3)
ALGRITHM 2
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Jyväskylä Summer School on Charge Density August
2007
XDPROP topological analysis
Gradient vector plots show the division of the
molecule into atomic basins Also shows bond
paths and bcps
ODESOLVE rk bs eps 1e-6 stepi 0.01 TRAJPLT
origin atom C(1) TRAJPLT xaxis atom N(1) Xdim1
-2.0 Xdim2 2.5 TRAJPLT yaxis atom H(3) Ydim1
-2.0 Ydim2 2.0 TRAJPLT params Circle 0.1 ATrad
0.05 CPrad 0.05 CPgrid 0.1 CPlim 0.01 TRAJPLT
mark atoms labels bonds cps basins
hbonds TRAJPLT plot plane npath 36 zcut 0.3
xytol 0.3 all select O(1)
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Jyväskylä Summer School on Charge Density August
2007
XDPROP calculation of charges
The concept of atomic charges is a central one in
chemistry. Unfortunately it is a very hazy
concept and not one deeply founded in quantum
mechanics. It is only through AIM theory that an
unambiguous definition of atomic charge has
achieved. AIM derived charges are often larger
than chemical intuition expects and this
has led to considerable criticism.
XDPROP provides several ways to calculate net
atomic charges (a) directly from the refined
valence populations of the atoms (b) using
Hirshfelds stockholders approach (c) using a
fit to the electrostatic potential (d) using
Baders Quantum Theory of Atoms in Molecules
(AIM)
! Atomic/Molecular moments from pseudoatoms
MULTMOM ! ! Atomic/Molecular from STOCKHOLDER
partitioning STOCKMOM atoms all select ato(1)
ato(2) ... ! Atomic charges fitting electrostatic
potential QFIT grid 11 length 7.0 width 1.0
constrain false CONSTRAIN ato(1) ato(2) ...
R. F. W. Bader and C. Matta (2004) J. Phys Chem
A. 108, 8385 F. L. Hirshfeld (1977). Theor.
Chim. Acta, 44, 129
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Jyväskylä Summer School on Charge Density August
2007
XDPROP electrostatic potential
XDPROP can calculate maps of the electrostatic
potential. These may be used to show sites of
chemical reactivity. In general (and always for
isolated atoms) the ESP is positive, but on
chemical bond formation, some areas might achieve
a negative potential. One visually attractive way
of displaying the ESP is as a colour coded
isosurface (usually of the density).
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Jyväskylä Summer School on Charge Density August
2007
XDPROP d-orbital populations
The multipole populations can be directly related
to the d-orbital populations in transition metal
compounds. Not unique, but depends on the chosen
local coordinate system. Usually best if this
system is chosen to correspond to symmetry axes
(actual or idealised) of the compound. An optimal
coordinate system minimises the cross populations.
A. Holladay, P. C. Leung P. Coppens (1983)
Acta Cryst. A39, 377 J. R. Sabino P. Coppens
(2003). Acta Cryst. A59, 127
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Jyväskylä Summer School on Charge Density August
2007
Geometry calculations XDGEOM
Geometry calculations carried out using XDGEOM.
Uses variance- covariance matrix xd.cov (if
available) to determine correct sus for derived
parameters, distances, angles, torsions

• Provides
• Table of xyz, Uijs, distances, angles, torsions
• Tables of multipole parameters
• Writes a CIF xd_geo.cif of same (some will be
  moved to xd_lsm.cif in due time. e.g. xyz, Uijs)
• Generally positional parameters (hence
  interatomic distances, angles) are not very
  sensitive to model (spherical or multipole), but
  of course .

Aromatic C-H SHELX (X-ray) 0.96Å
neutron 1.083Å
K2SO4 tutorial data set SHELX
XD S-O1 1.4837(4) 1.4838(3) S-O2 1.4717(4) 1.
4716(3) S-O3 1.4830(3) 1.4832(2)